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    Publication
    A fast algorithm to simulate the failure of a periodic elastic fibre composite
    (01-06-2019) ;
    Gupta, Ankit
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    Kachhwah, Uttam S.
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    Sheikh, Najam
    Monte-Carlo simulations of the fracture of elastic unidirectional model fibre composites are an important tool to understand composite reliability. On account of being computationally intensive, fracture simulations reported in the literature have been limited to simulation patches comprised of a few thousand fibres. While these limited patch sizes suffice to capture the dominant failure event when the fibre strength variability is low (synthetic fibres), they suffer from edge effects when the fibre strength variability is high (natural fibres). On the basis of recent algorithmic developments based on Fourier acceleration, a novel bisection based Monte Carlo failure simulation algorithm is presently proposed. This algorithm is used to obtain empirical strength distributions for model composites comprised of up to 2 20≈ 10 6 fibres, and spanning a wide range of fibre strength variabilities. These simulations yield empirical weakest-link strength distributions well into the lower tail. A stochastic model is proposed for the weakest-link event. The strength distribution predicted by this model fits the empirical distributions for any fibre strength variability.
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    Publication
    A fast algorithm for the elastic fields due to interacting fibre breaks in a periodic fibre composite
    (01-05-2018)
    Gupta, Ankit
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    Monte Carlo simulations of the failure of unidirectional fibre composites typically require numerous evaluations of the stress-state in partially damaged composite patches. In a simulated composite patch comprised of N fibres, of which Nb fibres are broken in a common cross-sectional plane transverse to the fibre direction, the stress overloads in the intact fibres are given by the weighted superposition of the unit break solutions associated with each of the breaks. Determining the weights involves solving Nb linear equations, and determining overloads in the intact fibres requires matrix-vector multiplication. These operations require O(Nb3), and O(NNb) floating point operations, respectively. These costs become prohibitive for large N, and Nb; they limit Monte Carlo failure simulations to composite patches of only a few thousand fibres. In the present work, a fast algorithm to determine the overloads in a partially damaged composite, requiring O(Nb1/3NlogN) floating point operations, is proposed. This algorithm is based on the discrete Fourier transform. The efficiency of the proposed method derives from the computational simplicity of weighted superposition in Fourier space. Computations of the stress state ahead of large circular clusters of breaks in composite patches comprised of about one million fibres are used to demonstrate the efficiency of the proposed algorithm.